Unifying atom-centered descriptions and message-passing machine learning schemes

Over the last decade, dozens of frameworks have been proposed to incorporate machine-learning (ML) techniques in the atomistic simulation toolbox, and in doing so, they have proven to be extremely successful in accelerating the understanding, design, and characterization of materials. Most of these frameworks can be broadly classified into two groups. On one hand, methods relying on physics-based features to represent the underlying structures can be expressed as hierarchical correlations of an atom-centered density (ACDC) imbued with the translational, permutational, and rotational symmetries of the target. Whereas, the alternative class of methods comprises of deep learning models based on the ideas of message-passing (MP) on an atomistic graph, which have been recently extended to integrate geometric equivariance to afford higher descriptive power.

In this talk, I will present a generalization of the ACDC framework to simultaneously include information on multiple centers and their connectivities. This extension naturally includes the essence of message-passing and serves to unify MP models within the parlance of ACDCs. I will show examples that highlight how a common language reveals close connections between independent developments and helps understand information propagation and identify the roles of different ingredients of successful ML models, leading to a unified and systematically understandable theory of atomistic ML.